As it transpired, the considerable expertise here couldn't answer this. But my son found an answer.
He used "Armour Etch" and coated the offending layer for 2-3 minutes, then promptly removed it. The screen is as clean as a (very thoroughly wiped) baby's bottom.

It turns out fingerprints degrade the Apple screen coating over time.
This Armour Etch is for engraving glass. It is thoroughly nasty stuff, the principal ingredient being ammonium. Warnings are given about eye cover, or letting it touch you anywhere. Even farting whie the bottle is open risks a chemical explosion

. But it works.